An efficient nonlinear iteration scheme for nonlinear parabolic-hyperbolic system

A nonlinear iteration method named the Picard-Newton iteration is studied for a two-dimensional nonlinear coupled parabolic-hyperbolic system. It serves as an efficient method to solve a nonlinear discrete scheme with second spatial and temporal accuracy. The nonlinear iteration scheme is constructed with a linearization-discretization approach through discretizing the linearized systems of the original nonlinear partial differential equations. It can be viewed as an improved Picard iteration, and can accelerate convergence over the standard Picard iteration. Moreover, the discretization with second-order accuracy in both spatial and temporal variants is introduced to get the Picard-Newton iteration scheme. By using the energy estimate and inductive hypothesis reasoning, the difficulties arising from the nonlinearity and the coupling of different equation types are overcome. It follows that the rigorous theoretical analysis on the approximation of the solution of the Picard-Newton iteration scheme to the solution of the original continuous problem is obtained, which is different from the traditional error estimate that usually estimates the error between the solution of the nonlinear discrete scheme and the solution of the original problem. Moreover, such approximation is independent of the iteration number. Numerical experiments verify the theoretical result, and show that the Picard-Newton iteration scheme with second-order spatial and temporal accuracy is more accurate and efficient than that of first-order temporal accuracy.     

奇异Hamilton-Jacobi-Bellman方程粘性解的存在唯一性

研究系数在边界点有奇性的一类Hamilt on- Jacobi- Bellman (HJB)方程的粘性解的存在唯一性问题及解的渐近估计,这类问题包括波动系数振荡或爆破的情况.奇异HJB方程在随机最优控制和金融数学等许多领域都有重要的应用,包括金融数学中的随机利率模型.应用粘性上下解理论建立了一类奇异HJB方程的比较原理,给出了粘性解存在唯一性的条件.     

基于时间序列模型的全国30家电台收视率分析

以湖南电视台和北京卫视为代表,对全国30家电视台卫星频道2008全年日收视率进行时间序列分析,建立了四种拟合模型.其中,大部分电台收视率具有长期趋势或长期趋势和季节效应的综合影响,分别建立ARIMA模型和乘积季节模型,并进行预测,其结果表明模型拟合效果较好.     

有理对称矩阵的准正交相似

对一个有理对称矩阵A,用线性代数的理论直接证明了存在准正交矩阵P使得P~(-1)AP成为A的有理标准形,并给出了P的算法.     

Cell compatible trimethoprim-decorated iron oxide nanoparticles bind dihydrofolate reductase for magnetically modulating focal adhesion of mammalian cells

On the basis of the high affinity binding of trimethoprim (TMP) to Escherichia coli dihydrofolate reductase (eDHFR), TMP-decorated iron oxide nanoparticles bind to eDHFR with high affinity and specificity, which allows magnetic modulation of focal adhesion of mammalian cells adhered to a surface. Besides being the first example of nanoparticles that selectively bind to eDHFR, the biocompatibility of the conjugate of TMP-iron oxide nanoparticles renders a convenient and versatile platform for investigating the cellular responses to specific, mechanical perturbation of proteins via a magnetic force.     

Rational design of 3D dendritic TiO2 nanostructures with favorable architectures

Controlling the morphology and size of titanium dioxide (TiO(2)) nanostructures is crucial to obtain superior photocatalytic, photovoltaic, and electrochemical properties. However, the synthetic techniques for preparing such structures, especially those with complex configurations, still remain a challenge because of the rapid hydrolysis of Ti-containing polymer precursors in aqueous solution. Herein, we report a completely novel approach-three-dimensional (3D) TiO(2) nanostructures with favorable dendritic architectures-through a simple hydrothermal synthesis. The size of the 3D TiO(2) dendrites and the morphology of the constituent nano-units, in the form of nanorods, nanoribbons, and nanowires, are controlled by adjusting the precursor hydrolysis rate and the surfactant aggregation. These novel configurations of TiO(2) nanostructures possess higher surface area and superior electrochemical properties compared to nanoparticles with smooth surfaces. Our findings provide an effective solution for the synthesis of complex TiO(2) nano-architectures, which can pave the way to further improve the energy storage and energy conversion efficiency of TiO(2)-based devices.     

Ocular Pharmacokinetic Study of l-Carnosine and N-Acetyl-l-carnosine in Rabbit by Microdialysis Coupled with UPLC-MS-MS

In order to provide useful information for rational drug design, the ocular pharmacokinetics of l-carnosine (CAR) and its acetylized prodrug N-acetyl-l-carnosine (NAC) were investigated. The in vivo microdialysis sampling coupled with ultra-performance liquid chromatography-tandem mass spectrometry (UPLC-MS-MS) was developed for continuously simultaneous monitoring of CAR and NAC in rabbit aqueous humor. The measured in vitro recoveries of the probe were 61.3% for CAR and 65.8% for NAC, while in vivo recoveries decreased to 43.1% for CAR and 43.0% for NAC, respectively. The method was sensitive with LLOQ 20.5 ng mL^?1 for CAR and 20.4 ng mL^?1 for NAC. The initial data indicated that the value of C _max and AUC_(0?C??) of NAC were higher than these of CAR (C _max 2305 vs. 1,802 ng mL^?1), (AUC_(0?C??) 1,337 vs. 1,891 ng h mL^?1), which indicated that the NAC exhibited better ocular bioavailability and duration. The method was rapid, specific and sensitive for continuously monitoring of aqueous humor and it was successfully applied to pharmacokinetic studies of CAR and NAC.     

Polyynes from Toona ciliata var. ciliata and Related Cytotoxic Activity

A phytochemical investigation of Toona ciliata var. ciliata afforded three new polyynes, 1 – 3 . Their structures were elucidated on the basis of spectroscopic analysis and chemical methods. Only compound 3 exhibited potent cytotoxicity against the HL‐60 cell line with an IC₅₀ value of 6.7±0.27 μM .     

Two New Cytotoxic Alkaloids from Mappianthus iodoides Hand.‐Mazz.

Two new alkaloids, mappine A ( 1 ) and mapposidic acid ( 2 ), together with eleven known compounds, were isolated from the stems of Mappianthus iodoides Hand.‐Mazz. Their structures were elucidated by means of spectroscopic and mass‐spectrometric analyses, particularly 1D‐ and 2D‐NMR spectroscopy. The cytotoxic activities of the two new alkaloids were also evaluated.